steve benoit department of mathematics colorado state university models of cell dynamics and...

STEVE BENOIT

DEPARTMENT OF MATHEMATICSCOLORADO STATE UNIVERSITY

Models of cell dynamics andintercellular communication

This program is based upon collaborative work supported by a National Science Foundation Grant No. 0841259; Colorado State University, Thomas Chen, Principal Investigator, Michael A. de Miranda and Stuart Tobet Co-Principal Investigators. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Modeling Cell Dynamics & Communication

OUTLINE:

Context – CSU research program

Observing cell motion – phenomenology &

analysis

Modeling cell behavior – top-down vs. bottom-

up

New approaches at mesoscopic scale

Results & discussion

CSU Cell Communication Research

Tissue Slice Preparation

Electrochemical

BiosensorDevelopment

MicrochipDevelopmen

t

FluorescenceVideo

MicroscopyOptical Image

Composite Image

Analysis

Analysis

Data Acquisition

& Processing

Microchip

Biosensor Array

Tissue Sample

Biomedical Sciences Chemistry

Electrical & Computer Engineering

Computer Science Mathematics

Chemical Image

Cell Motion Analysis from Optical Images

Automated analysis tool:

Raw Image

}

Merged Equalized}

Smoothed

}

Stabilized

}

Trajectories

Analysis

Z-planes

Cell Motion Analysis from Optical Images

Automated analysis tool:

2( ) 4r r Kt Best-fit curves for model:

α ≈ 1: diffusive behaviorα < 1: subdiffusive behaviorα > 1: superdiffusive behavior

Voronoi diagram and visualizations:

α K Speed DistanceVoronoi

α=.42 α=.93 α=1.25

Challenges of modeling cell behavior

Cell mechanics:

Microtubules

Actin Microfilaments

Intermediate Filaments

Membrane & AdhesionOrganelles

Challenges of modeling cell behavior

Examples of cell motion & signaling:

Neutrophil Macrophage Neuron T Cells

Examples of cell mechanics:

Actin-InducedMovement

Actin motility MicrotubuleDynamics

Adhesion

History: “Top-Down” Models

Continuum model of cell concentration (e.g. Keller & Segel -1971)

Random walk with bias (e.g. Alt – 1980)

Stochastic model(e.g. Tranquillo – 1988)

Hyperbolic continuum model(e.g. Hillen & Stevens - 2000)

History: “Bottom-Up” Models

Molecular dynamics models(~ 7x1015 atoms per cell)

Membrane models

Cytoskeleton models

Adhesion modulation models

Mechanical Components

Models for Mesoscopic Simulation

Plasma Membrane

Triangulation

Disc Model

Energy Functional Terms: Axial displacement Normal averaging

Radial Lennard-Jones

Each disc acts as sensor

~500-1000 discs per cell

Simulation

Models for Mesoscopic Simulation

Organelles

Interaction Terms:Simple Lennard-Jones

Organelles are treated just as membranes

Different energy parameters

Simulation

Models for Mesoscopic Simulation

Cytoskeleton

Interaction Terms:Simple Lennard-Jones

Collection of Lennard-Jones spheres

Interacts with other actin spheres and membrane discs

Models for Mesoscopic Simulation

Cytoskeleton Dynamics & SignalingMembrane discs are activated

by signals

Actin spheres close to activated discs are activated / created

Activated spheres grow (polymerize) then divide

Global rate of sphere shrinkage (depolymerization) to restore monomer pool

Signals (Diffusive)

Simulation

Directions for Future Work

Parallelization and optimization

Simulations with 1000-5000 cells

Mitosos and apoptosis

Boundary/interior conditions (ventricle, radial

glia)

Acknowledgements

Colorado State University Tom Chen, Michael de Miranda

CSU Biomedical Sciences Department and the Tobet Lab Stuart Tobet, Matt Stratton, Krystle Frahm, Brian Searcy

CSU Department of Mathematics Vakhtang Putkaradze

University of Ljubljana & Jožef Stefan Institute Primož Ziherl

The author would like to thank the National Science Foundation for support under Grant No. 0841259.